Proceedings of the Japan Academy, Series A, Mathematical Sciences

Telescopic approach to a formula of ${_{2}}F_{1}$-series by Gosper and Ebisu

Wenchang Chu

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By means of the telescoping method, we prove an infinite series identity with four free parameters. Its limiting case is utilized, with the help of the Pfaff transformation, not only to present a new proof for a ${_{2}}F_{1}$-series identity conjectured by Gosper (1977) and proved recently by Ebisu (2013), but also to establish an extension of the binomial series.

Article information

Proc. Japan Acad. Ser. A Math. Sci. Volume 93, Number 3 (2017), 13-15.

First available in Project Euclid: 2 March 2017

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Digital Object Identifier

Primary: 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 05A19: Combinatorial identities, bijective combinatorics

Classical hypergeometric series binomial series telescoping method Pfaff transformation


Chu, Wenchang. Telescopic approach to a formula of ${_{2}}F_{1}$-series by Gosper and Ebisu. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 3, 13--15. doi:10.3792/pjaa.93.13.

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